Variances and Covariances of Kendall's Tau and Their Estimation
- 1 October 1991
- journal article
- Published by Taylor & Francis in Multivariate Behavioral Research
- Vol. 26 (4) , 693-707
- https://doi.org/10.1207/s15327906mbr2604_6
Abstract
We generalize the formulas derived by Daniels and Kendall (1947) for the variance of the sample tau correlation. It is assumed that multivariate data are sampled from a population, and sample taus between pairs of variables are being used to estimate their population counterparts. Expressions for the variance of tau-a are generalized to allow for ties on either variable, and we further provide an expression for the covariance between two taus, including the special case where there is a variable in common. Unbiased estimators of the variance and the covariances are also derived for use in small samples. The variances and covariances of tau-a are used to provide asymptotic variances for tau-b and Somers' d.Keywords
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